Kim-Sau Chung

On the Existence of Stable Roommate Matchings

Abstract This paper identifies a condition called “no odd rings” that is sufficient for the existence of stable roommate matchings in the weak preferences case. It shows that the process of allowing randomly chosen blocking pairs to match converges to a stable roommate matching with probability one as long as there are no odd rings. This random-paths-to-stability result generalizes that of Roth and Vande Vate (1990, Econometrica58, 1475–1480) and may not hold if there are odd rings. The “no odd rings” condition can also be used to prove a number of other sufficient conditions that are more economically interpretable. Journal of Economic Literature Classification Numbers: C78, D71.

Implementation with near-complete information

Many refinements of Nash equilibrium yield solution correspondences that do not have closed graph in the space of payoffs or information. This has significance for implementation theory, especially under complete information. If a planner is concerned that all equilibria of his mechanism yield a desired outcome, and entertains the possibility that players may have even the slightest uncertainty about payoffs, then the planner should insist on a solution concept with closed graph. We show that this requirement entails substantial restrictions on the set of implementable social choice rules. In particular, when preferences are strict (or more generally, hedonic), while almost any social choice function can be implemented in undominated Nash equilibrium, only monotonic social choice functions can be implemented in the closure of the undominated Nash correspondence. Copyright Econometric Society, 2002.

Mechanism design with tacit collusion

In the mechanism design literature, collusion is often modelled as agents signing side contracts. This modelling approach is in turn implicitly justified by some unspecified repeated-interaction story. In this paper, we first second-guess what kind of repeatedinteraction story these side-contract theorists (would admit that they) are having in mind. We then show that , within this repeated-interaction story, there is a big difference between communicative and tacit collusion. While communicative collusion hurts the mechanism designer, tacit collusion is exploitable *We are very grateful to Yeon-Koo Che, Jeffrey Ely, and Larry Samulson, whose many probing questions have forced us to rethink our original intuition. All errors are ours.

Designing property rights over land in rural China

After nearly four decades, Chinas rural land tenure arrangement remains by and large how it looked like at the beginning of the economic reform. Rural land remains collectively owned. Peasants contract land from collectives, with their tenure insecure, and their transfer rights restricted. If such an arrangement was deemed a historical legacy at the beginning of the reform, it now looks more and more like a constrained efficient design by historical accident. This article suggests the constraints against which this design may be constrained efficient, and provides a stylised model that matches a wide array of empirical patterns.